A116611 Positive integers n such that 13^n == 5 (mod n).

1, 2, 4, 44, 82, 236, 25433, 177764, 219244, 86150213, 107218402, 1260236441, 12856300141, 447650116364, 657175627369, 14543842704596, 125035120614917

Offset: 1

Author

Zak Seidov, Feb 19 2006

Keywords

• nonn

Comments

No other terms below 10^15.

Some larger terms: 99790373907467602, 846248577183963835642742, 273781047810302314432122404459324, 4174626353309446327489382394518975030641698849116, 211*(13^211-5)/12607932861823674049268705845744 (207 digits). - Max Alekseyev, Jun 29 2011

Examples

			44 is in this sequence because 13^44 = 10315908977942302627204470186314316211062255002161 = 234452476771415968800101595143507186615051250049*44 + 5 == 5 (mod 44).
		

Crossrefs

Solutions to 13^n == k (mod n): A001022 (k=0), A015963 (k=-1), A116621 (k=1), A116622 (k=2), A116629 (k=3), A116630 (k=4), this sequence (k=5), A116631 (k=6), A116632 (k=7), A295532 (k=8), A116636 (k=9), A116620(k=10), A116638 (k=11), A116639 (k=15).

Cf. A116609, A128121, A276740, A123091.

Programs

Mathematica

Join[{1, 2}, Select[Range[1000000], PowerMod[13, #, #] == 5 &]] (* Robert Price, Apr 10 2020 *)

PARI

is(n) = Mod(13,n)^n==5; \\ Charles R Greathouse IV, Jun 08 2015

Extensions

More terms from Ryan Propper, Apr 01 2006

Terms 1,2,4 are prepended and a(13)-a(17) are added by Max Alekseyev, Jun 29 2011, Nov 27 2017